The coordinates of a moving particle at any time t are given by x=αt3 and y=βt3. The speed of the particle at time t is given by . . .

Question : The coordinates of a moving particle at any time t are given by x=αt³ and y=βt³. The speed of the particle at time t is given by ________.

Doubt by Yashika

Solution : 
x=αt³
v_x = d(αt³)/dt
v_x = 3αt²

y=βt³
v_y=d(βt³)/dt
v_y=3βt²

Now
v = v_x i + v_y j
v = 3αt² i + 3βt² j
Speed of the particle means magnitude of v
v = √[v_x² + v_y²]
v = √[(3αt²)2 + (3βt²)]
v = √[9α²t⁴ + 9β²t⁴]
v = √9t⁴(α² + β²)
v = 3t²√(α² + β²)